Emotion is a central component of verbal communication between humans. Due to advances in machine learning and the development of affective computing, automatic emotion recognition is increasingly possible and sought after. To examine the connection between emotional speech and significant group dynamics perceptions, such as leadership and contribution, a new dataset (14 group meetings, 45 participants) is collected for analyzing collaborative group work based on the lunar survival task. To establish a training database, each participant's audio is manually annotated both categorically and along a three-dimensional scale with axes of activation, dominance, and valence and then converted to spectrograms. The performance of several neural network architectures for predicting speech emotion are compared for two tasks: categorical emotion classification and 3D emotion regression using multitask learning. Pretraining each neural network architecture on the well-known IEMOCAP (Interactive Emotional Dyadic Motion Capture) corpus improves the performance on this new group dynamics dataset. For both tasks, the two-dimensional convolutional long short-term memory network achieves the highest overall performance. By regressing the annotated emotions against post-task questionnaire variables for each participant, it is shown that the emotional speech content of a meeting can predict 71% of perceived group leaders and 86% of major contributors.